Henri & Renaud Lifchitz's PRP Top records

What is a PRP ?

A PRP is a probable prime number, a number that nobody knows how to prove or disprove its primality.
Here are some criterions that can be used to recognize these numbers :

- N does not have any prime factor up to 2^32.
- N cannot be trivially written into a product.
- Take 3 square-free consecutive bases such that (b1/N)=(b2/N)=(b3/N)= -1. N should be such that b1^((N-1)/2)=b2^((N-1)/2)=b3^((N-1)/2)= -1 (mod N).
- Take a prime base such that (b/N)= -1 and b<>b1<>b2<>b3. N should pass the strong test in base b.
- or more (if someone has got an idea) !!!

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1-250	251-500	501-750	751-1000	1001-1250	1251-1500	1501-1750	1751-2000
2001-2250	2251-2500	2501-2750	2751-3000	3001-3250	3251-3500	3501-3750	3751-4000
4001-4250	4251-4500	4501-4750	4751-5000	5001-5250	5251-5500	5501-5750	5751-6000
6001-6250	6251-6500	6501-6750	6751-7000	7001-7250	7251-7500	7501-7750	7751-8000
8001-8250	8251-8500	8501-8750	8751-9000	9001-9250	9251-9500	9501-9750	9751-10000

Rank	Probable prime	Digits (> 50000)	Who ?	When ?
9001	(50891^20431-1)/50890	96157	Serge Batalov	06/2022
9002	(50^56597+1)/51	96155	Robert Price	03/2014
9003	22313^20374+20374^22313	96149	Hans Havermann	12/2019
9004	22279^20668+20668^22279	96141	Hans Havermann	11/2019
9005	(41*10^96137-59)/9	96138	Robert Price	10/2017
9006	2^319353-110343	96135	Enzo Doria	05/2014
9007	11^92309-42	96130	Lelio R Paula	05/2016
9008	(21675^22171-1)/21674	96129	Serge Batalov	06/2022
9009	14^83869-13^83869	96125	Jean-Louis Charton	01/2009
9010	(7*10^96112+143)/3	96113	Robert Price	04/2016
9011	26731^3940+3940^26731	96112	Hans Havermann	07/2020
9012	22640^17583+17583^22640	96109	Hans Havermann	07/2020
9013	(19178^22441-1)/19177	96107	Serge Batalov	06/2022
9014	2^319237+65835	96100	Lelio R Paula	03/2016
9015	2^319194-1841	96087	Yves Minet	03/2013
9016	23949^10280+10280^23949	96084	Hans Havermann	07/2020
9017	(1927^29251-1)/1926	96083	Serge Batalov	06/2022
9018	20^73847-31	96078	Lelio R Paula	05/2016
9019	(60229^20101-1)/60228	96075	Serge Batalov	06/2022
9020	(28044^21601-1)/28043	96074	Serge Batalov	06/2022
9021	50^56543-49	96065	Norbert Schneider	09/2018
9022	2^319107-109555	96061	Enzo Doria	04/2014
9023	(3*2^319114-1)/2627	96060	Lelio R Paula	02/2014
9024	2^319098-112157	96059	Enzo Doria	06/2014
9025	15^81673+94	96055	Lelio R Paula	07/2016
9026	(85761^19471-1)/85760	96052	Serge Batalov	06/2022
9027	2^319074+1871749	96051	Enzo Doria	05/2016
9028	25670^5517+5517^25670	96050	Hans Havermann	06/2020
9029	6*10^96037+19	96038	Robert Price	11/2021
9030	2^319007-112111	96031	Enzo Doria	06/2014
9031	(57987^20161-1)/57986	96029	Serge Batalov	06/2022
9033	2^318946-1421	96013	Yves Minet	01/2013
9032	(68310^19861-1)/68309	96013	Serge Batalov	06/2022
9034	(20294^22291-1)/20293	96012	Serge Batalov	06/2022
9035	(304^38669-1)/303	96008	Serge Batalov	06/2022
9036	(1840^29401-1)/1839	95986	Serge Batalov	06/2022
9037	22830^16003+16003^22830	95982	Hans Havermann	02/2020
9038	2^318834-110411	95979	Enzo Doria	05/2014
9039	2^318831-1965	95978	Lelio R Paula	03/2016
9040	(5*10^95976+7)/3	95977	Erik Branger	03/2014
9041	(12797^23369-1)/12796	95975	Serge Batalov	06/2022
9042	(10534^23857-1)/10533	95963	Serge Batalov	06/2022
9043	22871^15696+15696^22871	95962	Hans Havermann	01/2020
9044	(2^318760+858)/2	95957	Stefano Morozzi	02/2021
9045	23167^13860+13860^23167	95953	Hans Havermann	01/2020
9046	(823^32911-1)/822	95946	Serge Batalov	06/2022
9048	5*3^201089-8	95945	Lelio R Paula	08/2014
9047	(81783^19531-1)/81782	95945	Serge Batalov	06/2022
9049	2^318711-139	95942	Lelio R Paula	11/2012
9050	2^318635-1167	95919	Lelio R Paula	03/2016
9051	15^81555+16	95917	Lelio R Paula	07/2016
9052	(37*10^95895+377)/9	95896	Robert Price	10/2017
9053	(22699*2^318527+1)/21	95890	Lelio R Paula	07/2014
9054	2^318496-97305	95877	Lelio R Paula	03/2016
9055	22129^21496+21496^22129	95871	Hans Havermann	07/2020
9057	2^318466+15015	95868	Lelio R Paula	03/2016
9056	24847^7216+7216^24847	95868	Hans Havermann	07/2020
9058	23706^11065+11065^23706	95866	Hans Havermann	07/2020
9059	(2863^27733-1)/2862	95865	Serge Batalov	06/2022
9060	6^123187-173129	95859	Mike Oakes	04/2011
9061	2^318423-487	95855	Yves Minet	03/2012
9062	10^95848+443709	95849	Patrick De Geest	10/2022
9063	10^95848-5000000001	95848	Robert Price	09/2022
9064	10^95848-61971	95848	Patrick De Geest	10/2022
9065	(2^318359+678)/2	95836	Stefano Morozzi	09/2020
9066	(10223*2^318350+1)/1563	95834	Lelio R Paula	07/2014
9067	(8060^24533-1)/8059	95831	Serge Batalov	06/2022
9068	(9853^23993-1)/9852	95814	Serge Batalov	06/2022
9070	(2^318267+2550)/2	95808	Stefano Morozzi	09/2020
9069	(5048^25873-1)/5047	95808	Serge Batalov	06/2022
9072	4*10^95799+13	95800	Robert Price	02/2021
9071	(65533^19891-1)/65532	95800	Serge Batalov	06/2022
9073	45369!2+1024	95787	Robert Price	02/2015
9074	3^200758-86	95786	Lelio R Paula	05/2016
9075	(2^318271+1)/(346031404238891654090604244843)	95781	Gord Palameta	12/2018
9076	(2^318171+2030)/2	95779	Stefano Morozzi	09/2020
9077	3*10^95776-59	95777	Robert Price	10/2017
9078	(82970^19471-1)/82969	95772	Serge Batalov	06/2022
9079	193^41901-2	95768	Lelio R Paula	10/2017
9080	(2^318124+2502)/2	95765	Stefano Morozzi	09/2020
9081	(12900^23297-1)/12899	95761	Serge Batalov	06/2022
9082	4*10^95752-71	95753	Robert Price	11/2017
9083	(16955^22639-1)/16954	95743	Serge Batalov	06/2022
9084	(81795^19489-1)/81794	95740	Serge Batalov	06/2022
9085	(2742^27847-1)/2741	95737	Serge Batalov	06/2022
9086	(6072^25303-1)/6071	95726	Serge Batalov	06/2022
9087	23640^11197+11197^23640	95721	Hans Havermann	12/2019
9088	10^95712+89329	95713	Patrick De Geest	09/2022
9090	10^95712-4000001	95712	Robert Price	07/2021
9089	10^95712-989313	95712	Patrick De Geest	09/2022
9091	(60657^20011-1)/60656	95706	Serge Batalov	06/2022
9092	((10^47850-1)10000/9+6421)10^47850+(10^47850-1)/9	95704	Hans Havermann	05/2019
9093	(509203*2^317881-1)/52805	95693	Lelio R Paula	04/2015
9094	(26161^21661-1)/26160	95687	Serge Batalov	06/2022
9095	(2^317853+1086)/2	95683	Stefano Morozzi	09/2020
9096	4*10^95672+91	95673	Robert Price	11/2017
9097	6*10^95665+43	95666	Robert Price	07/2020
9098	(20819^22153-1)/20818	95663	Serge Batalov	06/2022
9099	(64464^19891-1)/64463	95658	Serge Batalov	06/2022
9100	(934^32203-1)/933	95652	Serge Batalov	06/2022
9101	(11*10^95641-113)/3	95642	Robert Price	01/2017
9102	(72330^19681-1)/72329	95632	Serge Batalov	06/2022
9103	(13224^23203-1)/13223	95624	Serge Batalov	06/2022
9104	(18211^22441-1)/18210	95602	Serge Batalov	06/2022
9105	(71975^19681-1)/71974	95590	Serge Batalov	06/2022
9106	(13*10^95588+11)/3	95589	Robert Price	05/2015
9107	Phi(191188,10)/191189	95587	Maksym Voznyy	11/2015
9108	(13368^23167-1)/13367	95585	Serge Batalov	06/2022
9109	(25874^21661-1)/25873	95583	Serge Batalov	06/2022
9110	3^200325+70	95580	Lelio R Paula	05/2016
9111	(25*10^95574-7)/9	95575	Robert Price	12/2014
9112	(2^317485-3)/21313	95569	Lelio R Paula	06/2013
9113	2^317464+31	95567	Lelio R Paula	11/2012
9114	(2^317451+2114)/2	95562	Stefano Morozzi	09/2020
9115	7^113073+82	95558	Lelio R Paula	04/2016
9116	(24728^21751-1)/24727	95552	Serge Batalov	06/2022
9117	(49764^20341-1)/49763	95536	Serge Batalov	06/2022
9118	(36155^20959-1)/36154	95531	Serge Batalov	06/2022
9119	(7725^24571-1)/7724	95526	Serge Batalov	06/2022
9120	(20546^22147-1)/20545	95510	Serge Batalov	06/2022
9121	2^317251+465	95503	Lelio R Paula	03/2016
9122	19^74684+58	95503	Lelio R Paula	06/2016
9123	(2^317250-7)/339	95500	Lelio R Paula	07/2013
9124	5*10^95498-21	95499	Robert Price	12/2021
9125	(21615^22031-1)/21614	95495	Serge Batalov	06/2022
9126	6^122718-79	95494	Lelio R Paula	05/2016
9127	22168^20291+20291^22168	95485	Hans Havermann	10/2019
9128	(77427^19531-1)/77426	95481	Serge Batalov	06/2022
9129	(13026^23203-1)/13025	95472	Serge Batalov	06/2022
9130	2^317141-110491	95469	Enzo Doria	05/2014
9131	(2^317097+3014)/2	95456	Stefano Morozzi	09/2020
9132	2^317094+76309	95455	Enzo Doria	05/2016
9133	2^317085+95	95453	Lelio R Paula	11/2012
9134	(17*10^95451-377)/9	95452	Robert Price	11/2017
9135	2^317057-109551	95444	Enzo Doria	04/2014
9136	3^200026+28	95437	Lelio R Paula	05/2016
9137	2^317024+93	95434	Donovan Johnson	06/2008
9138	(86*10^95428-437)/9	95429	Robert Price	03/2021
9139	10^95427+192591	95428	Patrick De Geest	05/2021
9142	2^316999+1605	95427	Lelio R Paula	03/2016
9141	(2^317000+3210)/2	95427	Stefano Morozzi	09/2020
9140	10^95427-10001	95427	Robert Price	02/2021
9143	2^316995-110427	95426	Enzo Doria	05/2014
9144	(69841^19699-1)/69840	95420	Serge Batalov	06/2022
9145	(59242^19993-1)/59241	95415	Serge Batalov	06/2022
9147	22300^18987+18987^22300	95410	Hans Havermann	06/2020
9146	(9478^23993-1)/9477	95410	Serge Batalov	06/2022
9148	2^316937+177	95408	Lelio R Paula	11/2012
9149	4*10^95407+91	95408	Robert Price	11/2017
9150	2^316908+1915	95399	Lelio R Paula	03/2016
9151	2^316894+99	95395	Lelio R Paula	11/2012
9152	(2^316887+2546)/2	95393	Stefano Morozzi	09/2020
9153	2*10^95374-21	95375	Robert Price	09/2020
9154	6^122547+11	95361	Lelio R Paula	05/2016
9155	2^316771+82875	95358	Lelio R Paula	03/2016
9156	(15609^22741-1)/15608	95358	Serge Batalov	06/2022
9157	(2^316765+3102)/2	95356	Stefano Morozzi	09/2020
9158	(2267^28411-1)/2266	95329	Serge Batalov	06/2022
9159	(824^32693-1)/823	95328	Serge Batalov	06/2022
9160	(23*10^95326+1)/3	95327	Serge Batalov	05/2009
9161	1*10^95326+57	95327	Robert Price	03/2011
9162	10^95326-393687	95326	Patrick De Geest	09/2013
9163	(3^199803+4)/479539	95325	Lelio R Paula	04/2013
9164	2^316654-109481	95323	Enzo Doria	04/2014
9165	8*10^95316+51	95317	Robert Price	05/2017
9166	(50^56099+43^56099)/93	95309	Serge Batalov	12/2016
9167	(23*2^316559+1)/3925	95292	Lelio R Paula	09/2013
9169	(71*10^95277-539)/9	95278	Robert Price	11/2017
9168	23422^11691+11691^23422	95278	Hans Havermann	10/2019
9170	19^74503-56	95271	Lelio R Paula	06/2016
9171	(5038^25733-1)/5037	95267	Serge Batalov	06/2022
9172	11^91475-4380	95262	Enzo Doria	01/2013
9173	(62*10^95251-611)/9	95252	Robert Price	05/2017
9174	(160090^18301-1)/160089	95240	Serge Batalov	06/2022
9175	(173205^18181-1)/173204	95238	Serge Batalov	06/2022
9176	(158710^18313-1)/158709	95234	Serge Batalov	06/2022
9177	(9979^23813-1)/9978	95227	Serge Batalov	06/2022
9178	(57376^20011-1)/57375	95223	Serge Batalov	06/2022
9179	(2^316321-509203)/69377	95218	Lelio R Paula	06/2013
9180	26541^3868+3868^26541	95216	Hans Havermann	07/2020
9181	(79*10^95214-43)/9	95215	Erik Branger	11/2013
9182	(7176^24691-1)/7175	95202	Anonymous	11/2020
9183	(9*2^316233-1)/1751	95194	Lelio R Paula	02/2014
9184	5*2^316213+9	95191	Lelio R Paula	08/2014
9185	2*10^95188-91	95189	Robert Price	04/2020
9186	2^316205-1848163	95188	Enzo Doria	07/2015
9187	2^316185-2787913	95182	Enzo Doria	04/2016
9188	(2^316174+3538)/2	95178	Stefano Morozzi	09/2020
9189	(9787*2^316142-1)/3	95172	Lelio R Paula	04/2015
9190	2^316140-5	95168	Henri Lifchitz	02/2006
9191	(15185*2^316117-1)/3	95165	Lelio R Paula	04/2015
9192	(34*10^95153-7)/9/19/19157	95149	Makoto Morimoto	05/2016
9193	2^316069+76817	95147	Enzo Doria	05/2016
9194	(199*10^95134-7)/3	95136	Robert Price	02/2017
9195	2^316027-97305	95134	Lelio R Paula	03/2016
9196	2^316006-2798051	95128	Enzo Doria	04/2016
9197	24994^6397+6397^24994	95127	Hans Havermann	02/2020
9199	2^315921-2797603	95102	Enzo Doria	04/2016
9198	(2^315921+1314)/2	95102	Stefano Morozzi	02/2021
9200	2*10^95095+63	95096	Robert Price	10/2017
9201	2^315857+1299	95083	Lelio R Paula	03/2016
9202	(2^315858+2598)/2	95083	Stefano Morozzi	09/2020
9204	14^82955-43	95078	Lelio R Paula	06/2016
9203	(8*10^95078-269)/9	95078	Robert Price	09/2021
9205	(23*10^95074-101)/3	95075	Robert Price	04/2021
9206	2^315827-933075	95074	Paul Bourdelais	04/2021
9207	(2*10^95072-17)/3	95072	Robert Price	08/2014
9208	(286*10^95059-1)/3	95061	Robert Price	11/2020
9209	(2^315779+1610)/2	95059	Stefano Morozzi	09/2020
9210	2^315775-111546435	95058	Paul Bourdelais	10/2021
9211	21938^21513+21513^21938	95051	Hans Havermann	09/2020
9212	2^315727+65	95044	Lelio R Paula	11/2012
9213	2^315725+1885757	95043	Enzo Doria	03/2017
9214	23277^12058+12058^23277	95000	Hans Havermann	09/2020
9215	1*10^94983+21	94984	Robert Price	03/2011
9216	10^94983-717	94983	Patrick De Geest	08/2013
9217	17^77187-82	94975	Lelio R Paula	07/2016
9218	3*10^94964+37	94965	Robert Price	10/2017
9219	(2^315481-1017)/20627285	94962	Lelio R Paula	06/2013
9220	2^315423-110329	94952	Enzo Doria	05/2014
9221	11^91169-7230	94943	Enzo Doria	02/2013
9222	7*10^94938+61	94939	Robert Price	02/2017
9223	2^315351+1025	94931	Lelio R Paula	03/2016
9224	2^315350-112253	94930	Enzo Doria	06/2014
9225	(2^315343+1766)/2	94928	Stefano Morozzi	09/2020
9226	(2^315343+3066)/2	94928	Stefano Morozzi	09/2020
9229	((1001327^(15817)+1)/1001328)	94906	Faysal YAtim	10/2010
9228	2^315268+7	94906	Lelio R Paula	10/2012
9227	11^91133+62	94906	Lelio R Paula	05/2016
9230	(2^315264+1558)/2	94904	Stefano Morozzi	09/2020
9231	30^64244+41	94897	Lelio R Paula	08/2012
9232	(151*10^94885-7)/9	94887	Robert Price	07/2017
9233	4^157583+22147	94875	Mike Oakes	01/2011
9234	(14*32^63026-190819)/31	94864	Eric Chen	04/2023
9235	2^315098+123	94854	Lelio R Paula	11/2012
9236	3^198791-34	94848	Robert Price	11/2013
9237	3*2^315067+7	94846	Lelio R Paula	08/2014
9238	(9*2^315057+1)/73	94841	Lelio R Paula	09/2013
9239	22576^15875+15875^22576	94836	Hans Havermann	09/2020
9240	(16*10^94822+53)/3	94823	Robert Price	12/2016
9241	8*6^121849-7	94818	Lelio R Paula	10/2014
9242	(85*10^94802+473)/9	94803	Robert Price	03/2017
9243	21767^21852-21852^21767	94790	Norbert Schneider	06/2020
9244	(2*34^61893-647)/3	94788	Eric Chen	03/2023
9245	2^314870-108761	94786	Enzo Doria	03/2014
9246	5*2^314841-3	94778	Lelio R Paula	08/2014
9248	(2^314842+550)/2	94777	Stefano Morozzi	09/2020
9247	11738^23289-23289^11738	94777	Norbert Schneider	05/2022
9249	(2^314787+2630)/2	94761	Stefano Morozzi	09/2020
9250	6^121772+113	94758	Lelio R Paula	05/2016

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